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arXiv 2105.04053physics.optics
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色散介质中光的协变理论

Covariant theory of light in a dispersive medium

Mikko Partanen, Jukka Tulkki

摘要:

在玻璃和其他低损耗色散介质中,不同波长的光以不同的相速度传播,光的能量和动量密度与时间和位置相关的相对论理论至今仍然是一个未解决的挑战。这是令人惊讶的麦克斯韦方程组的优秀的理论理解和色散介质中的光学现象的丰富的实验测量。这一挑战与分波干涉图样的复杂性以及光力对场和介质动力学的耦合有关。在这项工作中,我们使用光的质量极化理论[Phys. Rev. A 96,063834(2017)]来推导场和色散介质的应力-能量-动量(SEM)张量。我们的出发点,能量和动量的基本局部守恒定律,接近Philbin最近关于色散介质中的光的理论工作[Phys. Rev. A 83,013823(2011)],然而,它排除了描述场和介质之间耦合的功率转换和力密度源项。在一般的惯性系中,我们提出的SEM张量的洛伦兹标量,四矢量,和场张量,反映在一个透明的方式洛伦兹协方差的理论。场和介质的SEM张量是对称的、形状不变的,并且完全符合狭义相对论的协方差原理。光场-介质耦合态的SEM张量也具有零四发散度。因此,色散介质中的光具有明确的四动量和静止坐标系。光的总能量和动量密度的体积积分与具有非零静止质量的质量极化子准粒子模型一致。我们工作的预测可直接用于实验。

英文摘要:

The relativistic theory of the time- and position-dependent energy and momentum densities of light in glasses and other low-loss dispersive media, where different wavelengths of light propagate at different phase velocities, has remained a largely unsolved challenge until now. This is astonishing in view of the excellent theoretical understanding of Maxwell's equations and the abundant experimental measurements of optical phenomena in dispersive media. The challenge is related to the complexity of the interference patterns of partial waves and to the coupling of the field and medium dynamics by the optical force. In this work, we use the mass-polariton theory of light [Phys. Rev. A 96, 063834 (2017)] to derive the stress-energy-momentum (SEM) tensors of the field and the dispersive medium. Our starting point, the fundamental local conservation laws of energy and momentum, is close to that of a recent theoretical work on light in dispersive media by Philbin [Phys. Rev. A 83, 013823 (2011)], which however, excludes the power-conversion and force density source terms describing the coupling between the field and the medium. In the general inertial frame, we present the SEM tensors in terms of Lorentz scalars, four-vectors, and field tensors that reflect in a transparent way the Lorentz covariance of the theory. The SEM tensors of the field and the medium are symmetric, form-invariant, and in full accordance with the covariance principle of the special theory of relativity. The SEM tensor of the coupled field-medium state of light also has zero four-divergence. Therefore, light in a dispersive medium has well-defined four-momentum and rest frame. The volume integrals of the total energy and momentum densities of light agree with the model of mass-polariton quasiparticles having a nonzero rest mass. The predictions of our work are directly accessible to experiments.

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